---
title: "Two identical fixed point charges, each with positive charge \\(Q\\), are separated by a distance \\(2d\\) in vacuum. Point \\(P\\) is located at the midpoint between the two charges. A third positive point charge \\(q\\) is initially at rest at infinity and is slowly moved to point \\(P\\) by an external agent. Which expression represents the work done by the external agent on the charge \\(q\\)?"
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url: "https://nerd-notes.com/ubq/118051/"
date_modified: "2026-08-04T08:04:53+00:00"
---

# Two identical fixed point charges, each with positive charge \(Q\), are separated by a distance \(2d\) in vacuum. Point \(P\) is located at the midpoint between the two charges. A third positive point charge \(q\) is initially at rest at infinity and is slowly moved to point \(P\) by an external agent. Which expression represents the work done by the external agent on the charge \(q\)?

Two identical fixed point charges, each with positive charge \(Q\), are separated by a distance \(2d\) in vacuum. Point \(P\) is located at the midpoint between the two charges. A third positive point charge \(q\) is initially at rest at infinity and is slowly moved to point \(P\) by an external agent. Which expression represents the work done by the external agent on the charge \(q\)?

![A horizontal line segment showing two positive point charges labeled +Q at the left and right endpoints, separated by a distance 2d. Point P is marked with a black dot at the exact midpoint, a distance d from each charge. A curved dashed line with an arrow starts from an origin labeled infinity and ends at point P. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830693-7meT5z.jpg)

- **A.** \(\dfrac{1}{2\pi\varepsilon_0} \dfrac{q Q}{d}\)
- **B.** -\(\dfrac{1}{2\pi\varepsilon_0} \dfrac{q Q}{d}\)
- **C.** \(\dfrac{1}{4\pi\varepsilon_0} \dfrac{q Q}{d}\)
- **D.** \(0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118051/*